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**master_2m8** Question is :

5. Write down the probability distribution of a Poisson random variable with

parameter $\displaystyle \mu$

The average number of earthquakes in a certain region is 2 per week. Assume

that, in any time interval, the number of earthquakes occurring has a Poisson

distribution, calculate

(i) the probability of no earthquakes in a given week;

(ii) the probability of at least 1 earthquake in a given week;

(iii) the probability of at least 3 earthquakes in a given fortnight.

(iv) Calculate the probability that the time until the next earthquake, starting from now, is at least 1 week.

I need help on part (iv) my answers for the others parts are :

i) P(x=o) (e^-2 x 2^0)/0! =0.1353

ii) $\displaystyle P(x\geq1) =1-P(x\leq 0)

\Rightarrow 1-0.1353 =0.8647$

iii)$\displaystyle P(x\geq3)=1-P(x\leq2) $

$\displaystyle p(x\leq2)=P(x=0)+p(x=1)+p(x=2) =

1-P(x\leq2)=0.3233 $

these are my answers.

can someone please help me on part (iv)

thanks